Properties

Label 5415.g
Number of curves $2$
Conductor $5415$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 5415.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5415.g1 5415j2 \([0, 1, 1, -6250835, -6017354656]\) \(1590409933520896/45\) \(764260336845\) \([]\) \(73872\) \(2.2408\)  
5415.g2 5415j1 \([0, 1, 1, -77735, -8150461]\) \(3058794496/91125\) \(1547627182111125\) \([3]\) \(24624\) \(1.6915\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5415.g have rank \(1\).

Complex multiplication

The elliptic curves in class 5415.g do not have complex multiplication.

Modular form 5415.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{5} + 2 q^{7} + q^{9} - 3 q^{11} - 2 q^{12} - 4 q^{13} + q^{15} + 4 q^{16} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.